What is the Extension Produced in Springs Arranged in Series and Parallel?

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SUMMARY

The discussion focuses on calculating the extension produced by three different spring configurations: a single spring, springs in series, and springs in parallel. The formula used is Hooke's Law, represented as f = -kx, where k is the spring constant and x is the extension. For springs in parallel, the extension is halved due to shared load, while for springs in series, the equivalent spring constant must be calculated to determine the total extension. The key takeaway is that the extension in series depends on the combined effect of the individual spring constants.

PREREQUISITES
  • Understanding of Hooke's Law (f = -kx)
  • Knowledge of spring constants and their calculations
  • Concept of equivalent spring constants for series and parallel configurations
  • Basic principles of mechanical equilibrium
NEXT STEPS
  • Research how to calculate equivalent spring constants for springs in series and parallel
  • Explore the implications of Hooke's Law in real-world applications
  • Learn about the behavior of mechanical systems under load
  • Investigate the effects of varying spring constants on extension
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Students studying physics, particularly those focusing on mechanics and elasticity, as well as educators looking for clear explanations of spring behavior in different configurations.

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Homework Statement



I'm not so sure about the following:

You have 3 set-ups, using identical springs of the same length and stiffness. In the first you have a single spring with mass m attached to it, producing extension x. In the second you have identical springs in series, attached end to end and then with mass m attached to the bottom. In the third you have two identical springs in parallel, sharing mass m load.

What would be the extension produced in each set-up?

Homework Equations



f= -kx

The Attempt at a Solution



In the third case with the springs in parallel, since the whole thing is in equilibrium and assuming the length of the strings attaching the springs to the mass are the same, would the weight acting on them be halved, so the extension produced on each spring be x/2?

With the springs in series, I'm really not sure what to think. Not sure whether to treat the springs as one franken-spring, or think of spring 1 and spring 2.

Thanks for any help
 
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I suggest you try google: "equivalent spring constant" as a starting point. This may be helpful. Your equation is correct and the answer should depend on the value of k.
 

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